document.write( "Question 701011: Can someone please help me. I don't understand how to start these. \r
\n" ); document.write( "\n" ); document.write( "1. For the given equation, list the intercepts and test for symmetry.
\n" ); document.write( "y=x^2-5x-6\r
\n" ); document.write( "\n" ); document.write( "2. Write the equation of the circle in standard form.  Find the center, radius, intercepts, and graph the
\n" ); document.write( "circle.
\n" ); document.write( "x^2+y^2+14x-12y=-76 \n" ); document.write( "
Algebra.Com's Answer #432206 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
1.\r
\n" ); document.write( "\n" ); document.write( "\"+y=x%5E2-5x-6\"\r
\n" ); document.write( "\n" ); document.write( "the intercepts:\r
\n" ); document.write( "\n" ); document.write( "set \"x=0\" and find \"y-intercept\"\r
\n" ); document.write( "\n" ); document.write( "\"+y=0%5E2-5%2A0-6\"\r
\n" ); document.write( "\n" ); document.write( "\"+highlight%28y=-6%29\".......\"y-intercept\" is at (\"0\",\"-6\")\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "set \"y=0\" and find \"x-intercept\"\r
\n" ); document.write( "\n" ); document.write( "\"+0=x%5E2-5x-6\".....use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" ...in your case \"a=1\", \"b=-5\", and \"c=-6\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A%28-6%29+%29%29%2F%282%2A1%29+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+25%2B24+%29%29%2F2+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+sqrt%28+49+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B-+7%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%285+%2B7%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+12%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28x+=+6%29+\".......one \"x-intercept\"\r
\n" ); document.write( "\n" ); document.write( "and\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%285-7%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+-2%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28x+=-1%29+\".......another \"x-intercept\"\r
\n" ); document.write( "\n" ); document.write( "so, \"x-intercepts\" are at (\"6\",\"0\") and (\"-1\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "graph:\r
\n" ); document.write( "\n" ); document.write( " \"+graph%28600%2C+600%2C+-10%2C+10%2C+-15%2C+10%2C+x%5E2-5x-6%29+\" \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "parabola has an axis of symmetry which is the line that runs down its 'center' or vertex\r
\n" ); document.write( "\n" ); document.write( "since your equation is in standard form, then the formula for the axis of symmetry is:\r
\n" ); document.write( "\n" ); document.write( " \"x+=+-b%2F2a\" from the general standard form equation \"y+=+ax%5E2%2Bbx+%2B+c\"\r
\n" ); document.write( "\n" ); document.write( "so, plug in \"a=1\" and \"b=-5\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+-%28-5%29%2F2%2A1\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+5%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+2.5\"....so,axis of symmetry is a line parallel to \"y-axis\" and crosses \"x-axis\" at point (\"2.5\",\"0\")\r
\n" ); document.write( "\n" ); document.write( "let's see it on a graph:\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2By%5E2%2B14x-12y=-76\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2By%5E2%2B14x-12y%2B76=0\"......write \"76\" as \"49%2B36-9\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B14x%2By%5E2-12y%2B49%2B36-9=0\"...group \"49\" with \"x%5E2%2B14x\", and \"36\" with \"y%5E2-12y\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x%5E2%2B14x%2B49%29%2B%28y%5E2-12y%2B36%29-9=0\"...recognize square of the sum for \"x\" part and square of the difference for \"y\" part\r
\n" ); document.write( "\n" ); document.write( "\"%28x%2B7%29%5E2%2B%28y-6%29%5E2-9=0\".....move \"-9\" to the right\r
\n" ); document.write( "\n" ); document.write( "\"%28x%2B7%29%5E2%2B%28y-6%29%5E2=9\".........your answer for the equation of the circle in standard form \"+%28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2\"\r
\n" ); document.write( "\n" ); document.write( "as you can see \"h=-7\" and \"k=6\", so the center is at (\"-7\",\"6\")\r
\n" ); document.write( "\n" ); document.write( " radius is \"r=3\"\r
\n" ); document.write( "\n" ); document.write( " intercepts:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "set \"y=0\" and find \"x-intercepts\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x%2B7%29%5E2%2B%280-6%29%5E2=9\"\r
\n" ); document.write( "\n" ); document.write( "\"%28x%5E2%2B14x%2B49%29%2B%28-6%29%5E2=9\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B14x%2B49%2B36=9\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B14x%2B85-9=0\"\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2%2B14x%2B76=0\".......use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-14+%2B-+sqrt%28+14%5E2-4%2A1%2A76+%29%29%2F%282%2A1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-14+%2B-+sqrt%28+196-304+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-14+%2B-+sqrt%28-108+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-14+%2B-+10.39%2Ai%29%2F2+\"....as you can see, solution is complex, and it means there are \"no\" \"x-intercepts\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "set \"x=0\" and find \"y-intercepts\"\r
\n" ); document.write( "\n" ); document.write( "\"%280%2B7%29%5E2%2B%28y-6%29%5E2=9\"\r
\n" ); document.write( "\n" ); document.write( "\"49%2B%28y%5E2-12y%2B36%29-9=0\"\r
\n" ); document.write( "\n" ); document.write( "\"y%5E2-12y%2B36%2B49-9=0\"\r
\n" ); document.write( "\n" ); document.write( "\"y%5E2-12y%2B76=0\".......use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%28-12+%2B-+sqrt%28+12%5E2-4%2A1%2A76+%29%29%2F%282%2A1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%28-12+%2B-+sqrt%28+144-304+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%28-12+%2B-+sqrt%28-108+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-12+%2B-+10.39%2Ai%29%2F2+\"...solution is complex, and it means there are \"no\" \"y-intercepts\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "and graph of the circle:\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "
\n" );